Properties

Label 8007.2.a.f.1.14
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.44064 q^{2} -1.00000 q^{3} +0.0754557 q^{4} -3.22452 q^{5} +1.44064 q^{6} +1.08354 q^{7} +2.77258 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.44064 q^{2} -1.00000 q^{3} +0.0754557 q^{4} -3.22452 q^{5} +1.44064 q^{6} +1.08354 q^{7} +2.77258 q^{8} +1.00000 q^{9} +4.64538 q^{10} +4.97469 q^{11} -0.0754557 q^{12} +1.59786 q^{13} -1.56099 q^{14} +3.22452 q^{15} -4.14522 q^{16} -1.00000 q^{17} -1.44064 q^{18} +5.94298 q^{19} -0.243308 q^{20} -1.08354 q^{21} -7.16676 q^{22} +2.41663 q^{23} -2.77258 q^{24} +5.39750 q^{25} -2.30195 q^{26} -1.00000 q^{27} +0.0817590 q^{28} +1.75504 q^{29} -4.64538 q^{30} -2.72016 q^{31} +0.426617 q^{32} -4.97469 q^{33} +1.44064 q^{34} -3.49388 q^{35} +0.0754557 q^{36} -6.48548 q^{37} -8.56172 q^{38} -1.59786 q^{39} -8.94024 q^{40} -1.55199 q^{41} +1.56099 q^{42} -9.84359 q^{43} +0.375369 q^{44} -3.22452 q^{45} -3.48150 q^{46} -11.2096 q^{47} +4.14522 q^{48} -5.82595 q^{49} -7.77588 q^{50} +1.00000 q^{51} +0.120568 q^{52} -2.06350 q^{53} +1.44064 q^{54} -16.0410 q^{55} +3.00420 q^{56} -5.94298 q^{57} -2.52839 q^{58} +7.21706 q^{59} +0.243308 q^{60} +8.92460 q^{61} +3.91878 q^{62} +1.08354 q^{63} +7.67583 q^{64} -5.15232 q^{65} +7.16676 q^{66} -12.8646 q^{67} -0.0754557 q^{68} -2.41663 q^{69} +5.03344 q^{70} +9.11371 q^{71} +2.77258 q^{72} -10.7119 q^{73} +9.34326 q^{74} -5.39750 q^{75} +0.448432 q^{76} +5.39026 q^{77} +2.30195 q^{78} +11.7872 q^{79} +13.3663 q^{80} +1.00000 q^{81} +2.23587 q^{82} +10.6849 q^{83} -0.0817590 q^{84} +3.22452 q^{85} +14.1811 q^{86} -1.75504 q^{87} +13.7928 q^{88} +6.95174 q^{89} +4.64538 q^{90} +1.73134 q^{91} +0.182348 q^{92} +2.72016 q^{93} +16.1491 q^{94} -19.1632 q^{95} -0.426617 q^{96} -2.86124 q^{97} +8.39312 q^{98} +4.97469 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44064 −1.01869 −0.509345 0.860563i \(-0.670112\pi\)
−0.509345 + 0.860563i \(0.670112\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.0754557 0.0377279
\(5\) −3.22452 −1.44205 −0.721024 0.692911i \(-0.756328\pi\)
−0.721024 + 0.692911i \(0.756328\pi\)
\(6\) 1.44064 0.588141
\(7\) 1.08354 0.409538 0.204769 0.978810i \(-0.434356\pi\)
0.204769 + 0.978810i \(0.434356\pi\)
\(8\) 2.77258 0.980256
\(9\) 1.00000 0.333333
\(10\) 4.64538 1.46900
\(11\) 4.97469 1.49993 0.749963 0.661480i \(-0.230071\pi\)
0.749963 + 0.661480i \(0.230071\pi\)
\(12\) −0.0754557 −0.0217822
\(13\) 1.59786 0.443166 0.221583 0.975141i \(-0.428878\pi\)
0.221583 + 0.975141i \(0.428878\pi\)
\(14\) −1.56099 −0.417192
\(15\) 3.22452 0.832566
\(16\) −4.14522 −1.03630
\(17\) −1.00000 −0.242536
\(18\) −1.44064 −0.339563
\(19\) 5.94298 1.36341 0.681707 0.731626i \(-0.261238\pi\)
0.681707 + 0.731626i \(0.261238\pi\)
\(20\) −0.243308 −0.0544053
\(21\) −1.08354 −0.236447
\(22\) −7.16676 −1.52796
\(23\) 2.41663 0.503902 0.251951 0.967740i \(-0.418928\pi\)
0.251951 + 0.967740i \(0.418928\pi\)
\(24\) −2.77258 −0.565951
\(25\) 5.39750 1.07950
\(26\) −2.30195 −0.451449
\(27\) −1.00000 −0.192450
\(28\) 0.0817590 0.0154510
\(29\) 1.75504 0.325904 0.162952 0.986634i \(-0.447898\pi\)
0.162952 + 0.986634i \(0.447898\pi\)
\(30\) −4.64538 −0.848126
\(31\) −2.72016 −0.488555 −0.244277 0.969705i \(-0.578551\pi\)
−0.244277 + 0.969705i \(0.578551\pi\)
\(32\) 0.426617 0.0754159
\(33\) −4.97469 −0.865983
\(34\) 1.44064 0.247068
\(35\) −3.49388 −0.590574
\(36\) 0.0754557 0.0125760
\(37\) −6.48548 −1.06621 −0.533103 0.846050i \(-0.678974\pi\)
−0.533103 + 0.846050i \(0.678974\pi\)
\(38\) −8.56172 −1.38889
\(39\) −1.59786 −0.255862
\(40\) −8.94024 −1.41358
\(41\) −1.55199 −0.242380 −0.121190 0.992629i \(-0.538671\pi\)
−0.121190 + 0.992629i \(0.538671\pi\)
\(42\) 1.56099 0.240866
\(43\) −9.84359 −1.50113 −0.750566 0.660795i \(-0.770219\pi\)
−0.750566 + 0.660795i \(0.770219\pi\)
\(44\) 0.375369 0.0565890
\(45\) −3.22452 −0.480682
\(46\) −3.48150 −0.513319
\(47\) −11.2096 −1.63509 −0.817545 0.575865i \(-0.804665\pi\)
−0.817545 + 0.575865i \(0.804665\pi\)
\(48\) 4.14522 0.598311
\(49\) −5.82595 −0.832278
\(50\) −7.77588 −1.09967
\(51\) 1.00000 0.140028
\(52\) 0.120568 0.0167197
\(53\) −2.06350 −0.283443 −0.141722 0.989907i \(-0.545264\pi\)
−0.141722 + 0.989907i \(0.545264\pi\)
\(54\) 1.44064 0.196047
\(55\) −16.0410 −2.16296
\(56\) 3.00420 0.401453
\(57\) −5.94298 −0.787167
\(58\) −2.52839 −0.331994
\(59\) 7.21706 0.939582 0.469791 0.882778i \(-0.344329\pi\)
0.469791 + 0.882778i \(0.344329\pi\)
\(60\) 0.243308 0.0314109
\(61\) 8.92460 1.14268 0.571339 0.820714i \(-0.306424\pi\)
0.571339 + 0.820714i \(0.306424\pi\)
\(62\) 3.91878 0.497686
\(63\) 1.08354 0.136513
\(64\) 7.67583 0.959479
\(65\) −5.15232 −0.639067
\(66\) 7.16676 0.882167
\(67\) −12.8646 −1.57166 −0.785830 0.618443i \(-0.787764\pi\)
−0.785830 + 0.618443i \(0.787764\pi\)
\(68\) −0.0754557 −0.00915035
\(69\) −2.41663 −0.290928
\(70\) 5.03344 0.601611
\(71\) 9.11371 1.08160 0.540799 0.841152i \(-0.318122\pi\)
0.540799 + 0.841152i \(0.318122\pi\)
\(72\) 2.77258 0.326752
\(73\) −10.7119 −1.25373 −0.626866 0.779127i \(-0.715662\pi\)
−0.626866 + 0.779127i \(0.715662\pi\)
\(74\) 9.34326 1.08613
\(75\) −5.39750 −0.623249
\(76\) 0.448432 0.0514387
\(77\) 5.39026 0.614277
\(78\) 2.30195 0.260644
\(79\) 11.7872 1.32616 0.663082 0.748547i \(-0.269248\pi\)
0.663082 + 0.748547i \(0.269248\pi\)
\(80\) 13.3663 1.49440
\(81\) 1.00000 0.111111
\(82\) 2.23587 0.246910
\(83\) 10.6849 1.17282 0.586412 0.810013i \(-0.300540\pi\)
0.586412 + 0.810013i \(0.300540\pi\)
\(84\) −0.0817590 −0.00892064
\(85\) 3.22452 0.349748
\(86\) 14.1811 1.52919
\(87\) −1.75504 −0.188161
\(88\) 13.7928 1.47031
\(89\) 6.95174 0.736883 0.368441 0.929651i \(-0.379891\pi\)
0.368441 + 0.929651i \(0.379891\pi\)
\(90\) 4.64538 0.489666
\(91\) 1.73134 0.181494
\(92\) 0.182348 0.0190111
\(93\) 2.72016 0.282067
\(94\) 16.1491 1.66565
\(95\) −19.1632 −1.96611
\(96\) −0.426617 −0.0435414
\(97\) −2.86124 −0.290515 −0.145258 0.989394i \(-0.546401\pi\)
−0.145258 + 0.989394i \(0.546401\pi\)
\(98\) 8.39312 0.847833
\(99\) 4.97469 0.499975
\(100\) 0.407272 0.0407272
\(101\) 0.822654 0.0818572 0.0409286 0.999162i \(-0.486968\pi\)
0.0409286 + 0.999162i \(0.486968\pi\)
\(102\) −1.44064 −0.142645
\(103\) −3.10872 −0.306311 −0.153156 0.988202i \(-0.548944\pi\)
−0.153156 + 0.988202i \(0.548944\pi\)
\(104\) 4.43020 0.434417
\(105\) 3.49388 0.340968
\(106\) 2.97277 0.288741
\(107\) −10.7151 −1.03586 −0.517932 0.855422i \(-0.673298\pi\)
−0.517932 + 0.855422i \(0.673298\pi\)
\(108\) −0.0754557 −0.00726073
\(109\) −6.33348 −0.606637 −0.303319 0.952889i \(-0.598095\pi\)
−0.303319 + 0.952889i \(0.598095\pi\)
\(110\) 23.1093 2.20339
\(111\) 6.48548 0.615574
\(112\) −4.49150 −0.424407
\(113\) −9.64053 −0.906905 −0.453453 0.891280i \(-0.649808\pi\)
−0.453453 + 0.891280i \(0.649808\pi\)
\(114\) 8.56172 0.801879
\(115\) −7.79245 −0.726650
\(116\) 0.132428 0.0122956
\(117\) 1.59786 0.147722
\(118\) −10.3972 −0.957142
\(119\) −1.08354 −0.0993277
\(120\) 8.94024 0.816128
\(121\) 13.7476 1.24978
\(122\) −12.8572 −1.16403
\(123\) 1.55199 0.139938
\(124\) −0.205251 −0.0184321
\(125\) −1.28174 −0.114642
\(126\) −1.56099 −0.139064
\(127\) 12.5431 1.11302 0.556509 0.830842i \(-0.312140\pi\)
0.556509 + 0.830842i \(0.312140\pi\)
\(128\) −11.9114 −1.05283
\(129\) 9.84359 0.866679
\(130\) 7.42266 0.651010
\(131\) 14.3554 1.25424 0.627119 0.778924i \(-0.284234\pi\)
0.627119 + 0.778924i \(0.284234\pi\)
\(132\) −0.375369 −0.0326717
\(133\) 6.43944 0.558370
\(134\) 18.5333 1.60103
\(135\) 3.22452 0.277522
\(136\) −2.77258 −0.237747
\(137\) 5.93871 0.507378 0.253689 0.967286i \(-0.418356\pi\)
0.253689 + 0.967286i \(0.418356\pi\)
\(138\) 3.48150 0.296365
\(139\) −21.7332 −1.84339 −0.921694 0.387917i \(-0.873195\pi\)
−0.921694 + 0.387917i \(0.873195\pi\)
\(140\) −0.263633 −0.0222811
\(141\) 11.2096 0.944019
\(142\) −13.1296 −1.10181
\(143\) 7.94886 0.664717
\(144\) −4.14522 −0.345435
\(145\) −5.65917 −0.469968
\(146\) 15.4320 1.27716
\(147\) 5.82595 0.480516
\(148\) −0.489366 −0.0402257
\(149\) −0.666766 −0.0546236 −0.0273118 0.999627i \(-0.508695\pi\)
−0.0273118 + 0.999627i \(0.508695\pi\)
\(150\) 7.77588 0.634898
\(151\) 0.698424 0.0568370 0.0284185 0.999596i \(-0.490953\pi\)
0.0284185 + 0.999596i \(0.490953\pi\)
\(152\) 16.4774 1.33649
\(153\) −1.00000 −0.0808452
\(154\) −7.76545 −0.625758
\(155\) 8.77119 0.704519
\(156\) −0.120568 −0.00965313
\(157\) −1.00000 −0.0798087
\(158\) −16.9812 −1.35095
\(159\) 2.06350 0.163646
\(160\) −1.37563 −0.108753
\(161\) 2.61851 0.206367
\(162\) −1.44064 −0.113188
\(163\) −11.8082 −0.924893 −0.462447 0.886647i \(-0.653028\pi\)
−0.462447 + 0.886647i \(0.653028\pi\)
\(164\) −0.117107 −0.00914449
\(165\) 16.0410 1.24879
\(166\) −15.3932 −1.19474
\(167\) −10.5976 −0.820068 −0.410034 0.912070i \(-0.634483\pi\)
−0.410034 + 0.912070i \(0.634483\pi\)
\(168\) −3.00420 −0.231779
\(169\) −10.4468 −0.803604
\(170\) −4.64538 −0.356284
\(171\) 5.94298 0.454471
\(172\) −0.742755 −0.0566345
\(173\) −15.2338 −1.15821 −0.579104 0.815254i \(-0.696597\pi\)
−0.579104 + 0.815254i \(0.696597\pi\)
\(174\) 2.52839 0.191677
\(175\) 5.84839 0.442097
\(176\) −20.6212 −1.55438
\(177\) −7.21706 −0.542468
\(178\) −10.0150 −0.750655
\(179\) −13.0103 −0.972435 −0.486217 0.873838i \(-0.661624\pi\)
−0.486217 + 0.873838i \(0.661624\pi\)
\(180\) −0.243308 −0.0181351
\(181\) −23.2066 −1.72493 −0.862466 0.506115i \(-0.831081\pi\)
−0.862466 + 0.506115i \(0.831081\pi\)
\(182\) −2.49424 −0.184886
\(183\) −8.92460 −0.659726
\(184\) 6.70030 0.493953
\(185\) 20.9125 1.53752
\(186\) −3.91878 −0.287339
\(187\) −4.97469 −0.363786
\(188\) −0.845829 −0.0616884
\(189\) −1.08354 −0.0788157
\(190\) 27.6074 2.00285
\(191\) −14.9928 −1.08484 −0.542420 0.840107i \(-0.682492\pi\)
−0.542420 + 0.840107i \(0.682492\pi\)
\(192\) −7.67583 −0.553955
\(193\) 13.0199 0.937196 0.468598 0.883412i \(-0.344759\pi\)
0.468598 + 0.883412i \(0.344759\pi\)
\(194\) 4.12203 0.295945
\(195\) 5.15232 0.368965
\(196\) −0.439601 −0.0314001
\(197\) 11.4527 0.815971 0.407985 0.912988i \(-0.366231\pi\)
0.407985 + 0.912988i \(0.366231\pi\)
\(198\) −7.16676 −0.509320
\(199\) 7.91095 0.560793 0.280396 0.959884i \(-0.409534\pi\)
0.280396 + 0.959884i \(0.409534\pi\)
\(200\) 14.9650 1.05819
\(201\) 12.8646 0.907398
\(202\) −1.18515 −0.0833870
\(203\) 1.90166 0.133470
\(204\) 0.0754557 0.00528296
\(205\) 5.00442 0.349524
\(206\) 4.47856 0.312036
\(207\) 2.41663 0.167967
\(208\) −6.62347 −0.459255
\(209\) 29.5645 2.04502
\(210\) −5.03344 −0.347340
\(211\) −3.28941 −0.226452 −0.113226 0.993569i \(-0.536118\pi\)
−0.113226 + 0.993569i \(0.536118\pi\)
\(212\) −0.155703 −0.0106937
\(213\) −9.11371 −0.624461
\(214\) 15.4366 1.05522
\(215\) 31.7408 2.16470
\(216\) −2.77258 −0.188650
\(217\) −2.94739 −0.200082
\(218\) 9.12429 0.617975
\(219\) 10.7119 0.723842
\(220\) −1.21038 −0.0816040
\(221\) −1.59786 −0.107484
\(222\) −9.34326 −0.627079
\(223\) 15.2355 1.02024 0.510122 0.860102i \(-0.329600\pi\)
0.510122 + 0.860102i \(0.329600\pi\)
\(224\) 0.462255 0.0308857
\(225\) 5.39750 0.359833
\(226\) 13.8886 0.923855
\(227\) −2.95734 −0.196286 −0.0981429 0.995172i \(-0.531290\pi\)
−0.0981429 + 0.995172i \(0.531290\pi\)
\(228\) −0.448432 −0.0296981
\(229\) −1.99894 −0.132093 −0.0660467 0.997817i \(-0.521039\pi\)
−0.0660467 + 0.997817i \(0.521039\pi\)
\(230\) 11.2262 0.740231
\(231\) −5.39026 −0.354653
\(232\) 4.86601 0.319469
\(233\) 5.10521 0.334453 0.167227 0.985918i \(-0.446519\pi\)
0.167227 + 0.985918i \(0.446519\pi\)
\(234\) −2.30195 −0.150483
\(235\) 36.1456 2.35788
\(236\) 0.544569 0.0354484
\(237\) −11.7872 −0.765661
\(238\) 1.56099 0.101184
\(239\) −23.7050 −1.53335 −0.766674 0.642036i \(-0.778090\pi\)
−0.766674 + 0.642036i \(0.778090\pi\)
\(240\) −13.3663 −0.862792
\(241\) 29.6586 1.91048 0.955239 0.295834i \(-0.0955976\pi\)
0.955239 + 0.295834i \(0.0955976\pi\)
\(242\) −19.8054 −1.27314
\(243\) −1.00000 −0.0641500
\(244\) 0.673412 0.0431108
\(245\) 18.7859 1.20018
\(246\) −2.23587 −0.142554
\(247\) 9.49605 0.604219
\(248\) −7.54187 −0.478909
\(249\) −10.6849 −0.677130
\(250\) 1.84653 0.116785
\(251\) 6.58481 0.415629 0.207815 0.978168i \(-0.433365\pi\)
0.207815 + 0.978168i \(0.433365\pi\)
\(252\) 0.0817590 0.00515034
\(253\) 12.0220 0.755816
\(254\) −18.0701 −1.13382
\(255\) −3.22452 −0.201927
\(256\) 1.80839 0.113024
\(257\) −6.17406 −0.385127 −0.192564 0.981285i \(-0.561680\pi\)
−0.192564 + 0.981285i \(0.561680\pi\)
\(258\) −14.1811 −0.882877
\(259\) −7.02725 −0.436652
\(260\) −0.388772 −0.0241106
\(261\) 1.75504 0.108635
\(262\) −20.6810 −1.27768
\(263\) 18.8480 1.16222 0.581110 0.813825i \(-0.302619\pi\)
0.581110 + 0.813825i \(0.302619\pi\)
\(264\) −13.7928 −0.848885
\(265\) 6.65379 0.408739
\(266\) −9.27694 −0.568806
\(267\) −6.95174 −0.425440
\(268\) −0.970706 −0.0592953
\(269\) 7.85901 0.479172 0.239586 0.970875i \(-0.422988\pi\)
0.239586 + 0.970875i \(0.422988\pi\)
\(270\) −4.64538 −0.282709
\(271\) −19.5449 −1.18727 −0.593633 0.804736i \(-0.702307\pi\)
−0.593633 + 0.804736i \(0.702307\pi\)
\(272\) 4.14522 0.251341
\(273\) −1.73134 −0.104785
\(274\) −8.55557 −0.516861
\(275\) 26.8509 1.61917
\(276\) −0.182348 −0.0109761
\(277\) −15.9152 −0.956249 −0.478125 0.878292i \(-0.658683\pi\)
−0.478125 + 0.878292i \(0.658683\pi\)
\(278\) 31.3099 1.87784
\(279\) −2.72016 −0.162852
\(280\) −9.68708 −0.578914
\(281\) −7.55302 −0.450576 −0.225288 0.974292i \(-0.572332\pi\)
−0.225288 + 0.974292i \(0.572332\pi\)
\(282\) −16.1491 −0.961662
\(283\) −2.35210 −0.139818 −0.0699090 0.997553i \(-0.522271\pi\)
−0.0699090 + 0.997553i \(0.522271\pi\)
\(284\) 0.687682 0.0408064
\(285\) 19.1632 1.13513
\(286\) −11.4515 −0.677140
\(287\) −1.68164 −0.0992641
\(288\) 0.426617 0.0251386
\(289\) 1.00000 0.0588235
\(290\) 8.15285 0.478752
\(291\) 2.86124 0.167729
\(292\) −0.808273 −0.0473006
\(293\) 21.2244 1.23994 0.619972 0.784624i \(-0.287144\pi\)
0.619972 + 0.784624i \(0.287144\pi\)
\(294\) −8.39312 −0.489497
\(295\) −23.2715 −1.35492
\(296\) −17.9815 −1.04515
\(297\) −4.97469 −0.288661
\(298\) 0.960572 0.0556445
\(299\) 3.86143 0.223312
\(300\) −0.407272 −0.0235139
\(301\) −10.6659 −0.614772
\(302\) −1.00618 −0.0578992
\(303\) −0.822654 −0.0472603
\(304\) −24.6349 −1.41291
\(305\) −28.7775 −1.64780
\(306\) 1.44064 0.0823561
\(307\) −26.0338 −1.48583 −0.742914 0.669387i \(-0.766557\pi\)
−0.742914 + 0.669387i \(0.766557\pi\)
\(308\) 0.406726 0.0231754
\(309\) 3.10872 0.176849
\(310\) −12.6362 −0.717686
\(311\) 2.02959 0.115087 0.0575437 0.998343i \(-0.481673\pi\)
0.0575437 + 0.998343i \(0.481673\pi\)
\(312\) −4.43020 −0.250811
\(313\) −1.69194 −0.0956340 −0.0478170 0.998856i \(-0.515226\pi\)
−0.0478170 + 0.998856i \(0.515226\pi\)
\(314\) 1.44064 0.0813003
\(315\) −3.49388 −0.196858
\(316\) 0.889412 0.0500333
\(317\) 17.8299 1.00142 0.500712 0.865614i \(-0.333072\pi\)
0.500712 + 0.865614i \(0.333072\pi\)
\(318\) −2.97277 −0.166705
\(319\) 8.73081 0.488831
\(320\) −24.7508 −1.38361
\(321\) 10.7151 0.598056
\(322\) −3.77234 −0.210224
\(323\) −5.94298 −0.330676
\(324\) 0.0754557 0.00419198
\(325\) 8.62444 0.478398
\(326\) 17.0115 0.942179
\(327\) 6.33348 0.350242
\(328\) −4.30303 −0.237595
\(329\) −12.1460 −0.669632
\(330\) −23.1093 −1.27213
\(331\) −32.7132 −1.79808 −0.899039 0.437868i \(-0.855734\pi\)
−0.899039 + 0.437868i \(0.855734\pi\)
\(332\) 0.806239 0.0442481
\(333\) −6.48548 −0.355402
\(334\) 15.2674 0.835395
\(335\) 41.4820 2.26641
\(336\) 4.49150 0.245031
\(337\) 4.69479 0.255742 0.127871 0.991791i \(-0.459186\pi\)
0.127871 + 0.991791i \(0.459186\pi\)
\(338\) 15.0502 0.818622
\(339\) 9.64053 0.523602
\(340\) 0.243308 0.0131952
\(341\) −13.5320 −0.732796
\(342\) −8.56172 −0.462965
\(343\) −13.8974 −0.750388
\(344\) −27.2922 −1.47149
\(345\) 7.79245 0.419532
\(346\) 21.9465 1.17985
\(347\) 22.5102 1.20841 0.604205 0.796829i \(-0.293491\pi\)
0.604205 + 0.796829i \(0.293491\pi\)
\(348\) −0.132428 −0.00709889
\(349\) 11.0522 0.591613 0.295806 0.955248i \(-0.404412\pi\)
0.295806 + 0.955248i \(0.404412\pi\)
\(350\) −8.42545 −0.450359
\(351\) −1.59786 −0.0852874
\(352\) 2.12229 0.113118
\(353\) 3.52561 0.187649 0.0938246 0.995589i \(-0.470091\pi\)
0.0938246 + 0.995589i \(0.470091\pi\)
\(354\) 10.3972 0.552606
\(355\) −29.3873 −1.55972
\(356\) 0.524549 0.0278010
\(357\) 1.08354 0.0573469
\(358\) 18.7432 0.990609
\(359\) 2.47303 0.130522 0.0652608 0.997868i \(-0.479212\pi\)
0.0652608 + 0.997868i \(0.479212\pi\)
\(360\) −8.94024 −0.471192
\(361\) 16.3190 0.858896
\(362\) 33.4324 1.75717
\(363\) −13.7476 −0.721560
\(364\) 0.130639 0.00684737
\(365\) 34.5406 1.80794
\(366\) 12.8572 0.672055
\(367\) −21.7186 −1.13370 −0.566850 0.823821i \(-0.691838\pi\)
−0.566850 + 0.823821i \(0.691838\pi\)
\(368\) −10.0175 −0.522196
\(369\) −1.55199 −0.0807935
\(370\) −30.1275 −1.56625
\(371\) −2.23588 −0.116081
\(372\) 0.205251 0.0106418
\(373\) −0.199314 −0.0103201 −0.00516005 0.999987i \(-0.501643\pi\)
−0.00516005 + 0.999987i \(0.501643\pi\)
\(374\) 7.16676 0.370584
\(375\) 1.28174 0.0661888
\(376\) −31.0796 −1.60281
\(377\) 2.80431 0.144430
\(378\) 1.56099 0.0802887
\(379\) −10.2598 −0.527009 −0.263505 0.964658i \(-0.584878\pi\)
−0.263505 + 0.964658i \(0.584878\pi\)
\(380\) −1.44598 −0.0741770
\(381\) −12.5431 −0.642601
\(382\) 21.5993 1.10511
\(383\) −2.71079 −0.138515 −0.0692574 0.997599i \(-0.522063\pi\)
−0.0692574 + 0.997599i \(0.522063\pi\)
\(384\) 11.9114 0.607850
\(385\) −17.3810 −0.885817
\(386\) −18.7571 −0.954711
\(387\) −9.84359 −0.500378
\(388\) −0.215897 −0.0109605
\(389\) −13.7991 −0.699643 −0.349821 0.936816i \(-0.613758\pi\)
−0.349821 + 0.936816i \(0.613758\pi\)
\(390\) −7.42266 −0.375861
\(391\) −2.41663 −0.122214
\(392\) −16.1529 −0.815846
\(393\) −14.3554 −0.724134
\(394\) −16.4993 −0.831221
\(395\) −38.0080 −1.91239
\(396\) 0.375369 0.0188630
\(397\) −21.9553 −1.10190 −0.550952 0.834537i \(-0.685735\pi\)
−0.550952 + 0.834537i \(0.685735\pi\)
\(398\) −11.3969 −0.571273
\(399\) −6.43944 −0.322375
\(400\) −22.3738 −1.11869
\(401\) −18.9824 −0.947938 −0.473969 0.880542i \(-0.657179\pi\)
−0.473969 + 0.880542i \(0.657179\pi\)
\(402\) −18.5333 −0.924356
\(403\) −4.34643 −0.216511
\(404\) 0.0620740 0.00308830
\(405\) −3.22452 −0.160227
\(406\) −2.73961 −0.135964
\(407\) −32.2633 −1.59923
\(408\) 2.77258 0.137263
\(409\) 18.1615 0.898028 0.449014 0.893525i \(-0.351775\pi\)
0.449014 + 0.893525i \(0.351775\pi\)
\(410\) −7.20959 −0.356056
\(411\) −5.93871 −0.292935
\(412\) −0.234571 −0.0115565
\(413\) 7.81995 0.384795
\(414\) −3.48150 −0.171106
\(415\) −34.4537 −1.69127
\(416\) 0.681674 0.0334218
\(417\) 21.7332 1.06428
\(418\) −42.5919 −2.08324
\(419\) −6.78463 −0.331451 −0.165725 0.986172i \(-0.552997\pi\)
−0.165725 + 0.986172i \(0.552997\pi\)
\(420\) 0.263633 0.0128640
\(421\) 15.5643 0.758560 0.379280 0.925282i \(-0.376172\pi\)
0.379280 + 0.925282i \(0.376172\pi\)
\(422\) 4.73886 0.230684
\(423\) −11.2096 −0.545030
\(424\) −5.72123 −0.277847
\(425\) −5.39750 −0.261817
\(426\) 13.1296 0.636132
\(427\) 9.67013 0.467971
\(428\) −0.808512 −0.0390809
\(429\) −7.94886 −0.383775
\(430\) −45.7272 −2.20516
\(431\) 18.2215 0.877699 0.438849 0.898561i \(-0.355386\pi\)
0.438849 + 0.898561i \(0.355386\pi\)
\(432\) 4.14522 0.199437
\(433\) 23.7452 1.14112 0.570562 0.821255i \(-0.306726\pi\)
0.570562 + 0.821255i \(0.306726\pi\)
\(434\) 4.24614 0.203821
\(435\) 5.65917 0.271336
\(436\) −0.477897 −0.0228871
\(437\) 14.3620 0.687026
\(438\) −15.4320 −0.737370
\(439\) 0.570618 0.0272341 0.0136171 0.999907i \(-0.495665\pi\)
0.0136171 + 0.999907i \(0.495665\pi\)
\(440\) −44.4749 −2.12026
\(441\) −5.82595 −0.277426
\(442\) 2.30195 0.109492
\(443\) 33.3830 1.58607 0.793037 0.609173i \(-0.208498\pi\)
0.793037 + 0.609173i \(0.208498\pi\)
\(444\) 0.489366 0.0232243
\(445\) −22.4160 −1.06262
\(446\) −21.9489 −1.03931
\(447\) 0.666766 0.0315369
\(448\) 8.31705 0.392944
\(449\) 9.73144 0.459255 0.229627 0.973279i \(-0.426249\pi\)
0.229627 + 0.973279i \(0.426249\pi\)
\(450\) −7.77588 −0.366558
\(451\) −7.72068 −0.363553
\(452\) −0.727433 −0.0342156
\(453\) −0.698424 −0.0328148
\(454\) 4.26048 0.199954
\(455\) −5.58273 −0.261722
\(456\) −16.4774 −0.771625
\(457\) −2.66595 −0.124708 −0.0623541 0.998054i \(-0.519861\pi\)
−0.0623541 + 0.998054i \(0.519861\pi\)
\(458\) 2.87976 0.134562
\(459\) 1.00000 0.0466760
\(460\) −0.587985 −0.0274150
\(461\) 23.6917 1.10343 0.551717 0.834032i \(-0.313973\pi\)
0.551717 + 0.834032i \(0.313973\pi\)
\(462\) 7.76545 0.361281
\(463\) −6.56637 −0.305165 −0.152583 0.988291i \(-0.548759\pi\)
−0.152583 + 0.988291i \(0.548759\pi\)
\(464\) −7.27504 −0.337735
\(465\) −8.77119 −0.406754
\(466\) −7.35478 −0.340704
\(467\) −10.2933 −0.476319 −0.238160 0.971226i \(-0.576544\pi\)
−0.238160 + 0.971226i \(0.576544\pi\)
\(468\) 0.120568 0.00557324
\(469\) −13.9392 −0.643655
\(470\) −52.0729 −2.40194
\(471\) 1.00000 0.0460776
\(472\) 20.0099 0.921031
\(473\) −48.9688 −2.25159
\(474\) 16.9812 0.779971
\(475\) 32.0772 1.47180
\(476\) −0.0817590 −0.00374742
\(477\) −2.06350 −0.0944812
\(478\) 34.1505 1.56201
\(479\) 36.0257 1.64605 0.823027 0.568002i \(-0.192283\pi\)
0.823027 + 0.568002i \(0.192283\pi\)
\(480\) 1.37563 0.0627888
\(481\) −10.3629 −0.472507
\(482\) −42.7275 −1.94618
\(483\) −2.61851 −0.119146
\(484\) 1.03733 0.0471515
\(485\) 9.22612 0.418936
\(486\) 1.44064 0.0653489
\(487\) −29.1194 −1.31953 −0.659763 0.751474i \(-0.729343\pi\)
−0.659763 + 0.751474i \(0.729343\pi\)
\(488\) 24.7442 1.12012
\(489\) 11.8082 0.533987
\(490\) −27.0637 −1.22262
\(491\) 18.2037 0.821522 0.410761 0.911743i \(-0.365263\pi\)
0.410761 + 0.911743i \(0.365263\pi\)
\(492\) 0.117107 0.00527958
\(493\) −1.75504 −0.0790432
\(494\) −13.6804 −0.615511
\(495\) −16.0410 −0.720988
\(496\) 11.2756 0.506292
\(497\) 9.87504 0.442956
\(498\) 15.3932 0.689785
\(499\) −16.2743 −0.728539 −0.364270 0.931294i \(-0.618681\pi\)
−0.364270 + 0.931294i \(0.618681\pi\)
\(500\) −0.0967147 −0.00432521
\(501\) 10.5976 0.473467
\(502\) −9.48637 −0.423397
\(503\) −24.0561 −1.07261 −0.536305 0.844024i \(-0.680180\pi\)
−0.536305 + 0.844024i \(0.680180\pi\)
\(504\) 3.00420 0.133818
\(505\) −2.65266 −0.118042
\(506\) −17.3194 −0.769941
\(507\) 10.4468 0.463961
\(508\) 0.946447 0.0419918
\(509\) −24.7201 −1.09570 −0.547850 0.836576i \(-0.684554\pi\)
−0.547850 + 0.836576i \(0.684554\pi\)
\(510\) 4.64538 0.205701
\(511\) −11.6067 −0.513451
\(512\) 21.2175 0.937690
\(513\) −5.94298 −0.262389
\(514\) 8.89462 0.392325
\(515\) 10.0241 0.441715
\(516\) 0.742755 0.0326980
\(517\) −55.7644 −2.45251
\(518\) 10.1238 0.444813
\(519\) 15.2338 0.668691
\(520\) −14.2852 −0.626449
\(521\) −15.3498 −0.672489 −0.336244 0.941775i \(-0.609157\pi\)
−0.336244 + 0.941775i \(0.609157\pi\)
\(522\) −2.52839 −0.110665
\(523\) −1.62146 −0.0709016 −0.0354508 0.999371i \(-0.511287\pi\)
−0.0354508 + 0.999371i \(0.511287\pi\)
\(524\) 1.08320 0.0473197
\(525\) −5.84839 −0.255245
\(526\) −27.1533 −1.18394
\(527\) 2.72016 0.118492
\(528\) 20.6212 0.897422
\(529\) −17.1599 −0.746083
\(530\) −9.58574 −0.416378
\(531\) 7.21706 0.313194
\(532\) 0.485892 0.0210661
\(533\) −2.47986 −0.107415
\(534\) 10.0150 0.433391
\(535\) 34.5509 1.49376
\(536\) −35.6681 −1.54063
\(537\) 13.0103 0.561436
\(538\) −11.3220 −0.488128
\(539\) −28.9823 −1.24836
\(540\) 0.243308 0.0104703
\(541\) −37.5059 −1.61251 −0.806253 0.591572i \(-0.798508\pi\)
−0.806253 + 0.591572i \(0.798508\pi\)
\(542\) 28.1572 1.20946
\(543\) 23.2066 0.995890
\(544\) −0.426617 −0.0182911
\(545\) 20.4224 0.874799
\(546\) 2.49424 0.106744
\(547\) 11.7635 0.502970 0.251485 0.967861i \(-0.419081\pi\)
0.251485 + 0.967861i \(0.419081\pi\)
\(548\) 0.448110 0.0191423
\(549\) 8.92460 0.380893
\(550\) −38.6826 −1.64943
\(551\) 10.4302 0.444341
\(552\) −6.70030 −0.285184
\(553\) 12.7719 0.543115
\(554\) 22.9281 0.974121
\(555\) −20.9125 −0.887687
\(556\) −1.63990 −0.0695471
\(557\) 8.83557 0.374375 0.187188 0.982324i \(-0.440063\pi\)
0.187188 + 0.982324i \(0.440063\pi\)
\(558\) 3.91878 0.165895
\(559\) −15.7287 −0.665252
\(560\) 14.4829 0.612014
\(561\) 4.97469 0.210032
\(562\) 10.8812 0.458997
\(563\) 8.07419 0.340287 0.170143 0.985419i \(-0.445577\pi\)
0.170143 + 0.985419i \(0.445577\pi\)
\(564\) 0.845829 0.0356158
\(565\) 31.0861 1.30780
\(566\) 3.38854 0.142431
\(567\) 1.08354 0.0455043
\(568\) 25.2685 1.06024
\(569\) −8.32544 −0.349021 −0.174510 0.984655i \(-0.555834\pi\)
−0.174510 + 0.984655i \(0.555834\pi\)
\(570\) −27.6074 −1.15635
\(571\) −4.51807 −0.189075 −0.0945376 0.995521i \(-0.530137\pi\)
−0.0945376 + 0.995521i \(0.530137\pi\)
\(572\) 0.599787 0.0250783
\(573\) 14.9928 0.626333
\(574\) 2.42265 0.101119
\(575\) 13.0437 0.543962
\(576\) 7.67583 0.319826
\(577\) 36.5029 1.51963 0.759817 0.650137i \(-0.225288\pi\)
0.759817 + 0.650137i \(0.225288\pi\)
\(578\) −1.44064 −0.0599229
\(579\) −13.0199 −0.541090
\(580\) −0.427017 −0.0177309
\(581\) 11.5775 0.480316
\(582\) −4.12203 −0.170864
\(583\) −10.2653 −0.425144
\(584\) −29.6996 −1.22898
\(585\) −5.15232 −0.213022
\(586\) −30.5769 −1.26312
\(587\) −3.91386 −0.161542 −0.0807710 0.996733i \(-0.525738\pi\)
−0.0807710 + 0.996733i \(0.525738\pi\)
\(588\) 0.439601 0.0181288
\(589\) −16.1658 −0.666102
\(590\) 33.5260 1.38024
\(591\) −11.4527 −0.471101
\(592\) 26.8837 1.10491
\(593\) 5.82169 0.239068 0.119534 0.992830i \(-0.461860\pi\)
0.119534 + 0.992830i \(0.461860\pi\)
\(594\) 7.16676 0.294056
\(595\) 3.49388 0.143235
\(596\) −0.0503113 −0.00206083
\(597\) −7.91095 −0.323774
\(598\) −5.56295 −0.227486
\(599\) −27.4925 −1.12331 −0.561656 0.827371i \(-0.689836\pi\)
−0.561656 + 0.827371i \(0.689836\pi\)
\(600\) −14.9650 −0.610944
\(601\) 47.4556 1.93575 0.967876 0.251427i \(-0.0808999\pi\)
0.967876 + 0.251427i \(0.0808999\pi\)
\(602\) 15.3657 0.626261
\(603\) −12.8646 −0.523886
\(604\) 0.0527001 0.00214434
\(605\) −44.3292 −1.80224
\(606\) 1.18515 0.0481435
\(607\) −38.0691 −1.54518 −0.772588 0.634907i \(-0.781038\pi\)
−0.772588 + 0.634907i \(0.781038\pi\)
\(608\) 2.53538 0.102823
\(609\) −1.90166 −0.0770590
\(610\) 41.4582 1.67859
\(611\) −17.9114 −0.724617
\(612\) −0.0754557 −0.00305012
\(613\) −0.539040 −0.0217716 −0.0108858 0.999941i \(-0.503465\pi\)
−0.0108858 + 0.999941i \(0.503465\pi\)
\(614\) 37.5055 1.51360
\(615\) −5.00442 −0.201798
\(616\) 14.9450 0.602149
\(617\) −7.54171 −0.303618 −0.151809 0.988410i \(-0.548510\pi\)
−0.151809 + 0.988410i \(0.548510\pi\)
\(618\) −4.47856 −0.180154
\(619\) −8.96790 −0.360450 −0.180225 0.983625i \(-0.557683\pi\)
−0.180225 + 0.983625i \(0.557683\pi\)
\(620\) 0.661837 0.0265800
\(621\) −2.41663 −0.0969759
\(622\) −2.92391 −0.117238
\(623\) 7.53247 0.301782
\(624\) 6.62347 0.265151
\(625\) −22.8545 −0.914180
\(626\) 2.43748 0.0974213
\(627\) −29.5645 −1.18069
\(628\) −0.0754557 −0.00301101
\(629\) 6.48548 0.258593
\(630\) 5.03344 0.200537
\(631\) 2.30162 0.0916261 0.0458130 0.998950i \(-0.485412\pi\)
0.0458130 + 0.998950i \(0.485412\pi\)
\(632\) 32.6810 1.29998
\(633\) 3.28941 0.130742
\(634\) −25.6865 −1.02014
\(635\) −40.4453 −1.60502
\(636\) 0.155703 0.00617402
\(637\) −9.30904 −0.368838
\(638\) −12.5780 −0.497967
\(639\) 9.11371 0.360533
\(640\) 38.4084 1.51823
\(641\) 32.8329 1.29682 0.648412 0.761290i \(-0.275434\pi\)
0.648412 + 0.761290i \(0.275434\pi\)
\(642\) −15.4366 −0.609233
\(643\) 22.0372 0.869063 0.434531 0.900657i \(-0.356914\pi\)
0.434531 + 0.900657i \(0.356914\pi\)
\(644\) 0.197581 0.00778579
\(645\) −31.7408 −1.24979
\(646\) 8.56172 0.336856
\(647\) 6.27790 0.246810 0.123405 0.992356i \(-0.460619\pi\)
0.123405 + 0.992356i \(0.460619\pi\)
\(648\) 2.77258 0.108917
\(649\) 35.9027 1.40930
\(650\) −12.4248 −0.487339
\(651\) 2.94739 0.115517
\(652\) −0.891000 −0.0348942
\(653\) 11.5242 0.450978 0.225489 0.974246i \(-0.427602\pi\)
0.225489 + 0.974246i \(0.427602\pi\)
\(654\) −9.12429 −0.356788
\(655\) −46.2892 −1.80867
\(656\) 6.43334 0.251180
\(657\) −10.7119 −0.417910
\(658\) 17.4981 0.682147
\(659\) −8.75496 −0.341045 −0.170522 0.985354i \(-0.554546\pi\)
−0.170522 + 0.985354i \(0.554546\pi\)
\(660\) 1.21038 0.0471141
\(661\) −1.74453 −0.0678543 −0.0339271 0.999424i \(-0.510801\pi\)
−0.0339271 + 0.999424i \(0.510801\pi\)
\(662\) 47.1280 1.83168
\(663\) 1.59786 0.0620557
\(664\) 29.6249 1.14967
\(665\) −20.7641 −0.805196
\(666\) 9.34326 0.362044
\(667\) 4.24129 0.164223
\(668\) −0.799651 −0.0309394
\(669\) −15.2355 −0.589038
\(670\) −59.7609 −2.30876
\(671\) 44.3972 1.71393
\(672\) −0.462255 −0.0178319
\(673\) −15.4975 −0.597387 −0.298693 0.954349i \(-0.596551\pi\)
−0.298693 + 0.954349i \(0.596551\pi\)
\(674\) −6.76352 −0.260521
\(675\) −5.39750 −0.207750
\(676\) −0.788274 −0.0303182
\(677\) −14.2413 −0.547339 −0.273669 0.961824i \(-0.588237\pi\)
−0.273669 + 0.961824i \(0.588237\pi\)
\(678\) −13.8886 −0.533388
\(679\) −3.10026 −0.118977
\(680\) 8.94024 0.342842
\(681\) 2.95734 0.113326
\(682\) 19.4947 0.746492
\(683\) −11.0917 −0.424412 −0.212206 0.977225i \(-0.568065\pi\)
−0.212206 + 0.977225i \(0.568065\pi\)
\(684\) 0.448432 0.0171462
\(685\) −19.1495 −0.731663
\(686\) 20.0212 0.764413
\(687\) 1.99894 0.0762642
\(688\) 40.8038 1.55563
\(689\) −3.29718 −0.125613
\(690\) −11.2262 −0.427372
\(691\) −28.9163 −1.10003 −0.550014 0.835155i \(-0.685378\pi\)
−0.550014 + 0.835155i \(0.685378\pi\)
\(692\) −1.14948 −0.0436967
\(693\) 5.39026 0.204759
\(694\) −32.4292 −1.23099
\(695\) 70.0791 2.65825
\(696\) −4.86601 −0.184446
\(697\) 1.55199 0.0587859
\(698\) −15.9223 −0.602669
\(699\) −5.10521 −0.193097
\(700\) 0.441294 0.0166794
\(701\) 25.4593 0.961583 0.480791 0.876835i \(-0.340349\pi\)
0.480791 + 0.876835i \(0.340349\pi\)
\(702\) 2.30195 0.0868814
\(703\) −38.5431 −1.45368
\(704\) 38.1849 1.43915
\(705\) −36.1456 −1.36132
\(706\) −5.07915 −0.191156
\(707\) 0.891376 0.0335237
\(708\) −0.544569 −0.0204661
\(709\) 14.6781 0.551246 0.275623 0.961266i \(-0.411116\pi\)
0.275623 + 0.961266i \(0.411116\pi\)
\(710\) 42.3367 1.58887
\(711\) 11.7872 0.442055
\(712\) 19.2743 0.722334
\(713\) −6.57361 −0.246184
\(714\) −1.56099 −0.0584186
\(715\) −25.6312 −0.958553
\(716\) −0.981701 −0.0366879
\(717\) 23.7050 0.885279
\(718\) −3.56276 −0.132961
\(719\) 2.04707 0.0763429 0.0381715 0.999271i \(-0.487847\pi\)
0.0381715 + 0.999271i \(0.487847\pi\)
\(720\) 13.3663 0.498133
\(721\) −3.36841 −0.125446
\(722\) −23.5099 −0.874948
\(723\) −29.6586 −1.10302
\(724\) −1.75107 −0.0650780
\(725\) 9.47285 0.351813
\(726\) 19.8054 0.735046
\(727\) 17.3293 0.642709 0.321354 0.946959i \(-0.395862\pi\)
0.321354 + 0.946959i \(0.395862\pi\)
\(728\) 4.80028 0.177910
\(729\) 1.00000 0.0370370
\(730\) −49.7608 −1.84173
\(731\) 9.84359 0.364078
\(732\) −0.673412 −0.0248900
\(733\) −17.7168 −0.654386 −0.327193 0.944957i \(-0.606103\pi\)
−0.327193 + 0.944957i \(0.606103\pi\)
\(734\) 31.2887 1.15489
\(735\) −18.7859 −0.692927
\(736\) 1.03097 0.0380022
\(737\) −63.9974 −2.35737
\(738\) 2.23587 0.0823034
\(739\) −33.0929 −1.21734 −0.608671 0.793423i \(-0.708297\pi\)
−0.608671 + 0.793423i \(0.708297\pi\)
\(740\) 1.57797 0.0580073
\(741\) −9.49605 −0.348846
\(742\) 3.22110 0.118250
\(743\) −30.0436 −1.10219 −0.551096 0.834442i \(-0.685790\pi\)
−0.551096 + 0.834442i \(0.685790\pi\)
\(744\) 7.54187 0.276498
\(745\) 2.15000 0.0787698
\(746\) 0.287141 0.0105130
\(747\) 10.6849 0.390941
\(748\) −0.375369 −0.0137249
\(749\) −11.6102 −0.424226
\(750\) −1.84653 −0.0674259
\(751\) −8.16981 −0.298121 −0.149060 0.988828i \(-0.547625\pi\)
−0.149060 + 0.988828i \(0.547625\pi\)
\(752\) 46.4663 1.69445
\(753\) −6.58481 −0.239964
\(754\) −4.04002 −0.147129
\(755\) −2.25208 −0.0819616
\(756\) −0.0817590 −0.00297355
\(757\) 39.9107 1.45058 0.725289 0.688444i \(-0.241706\pi\)
0.725289 + 0.688444i \(0.241706\pi\)
\(758\) 14.7807 0.536859
\(759\) −12.0220 −0.436370
\(760\) −53.1317 −1.92729
\(761\) −21.7192 −0.787320 −0.393660 0.919256i \(-0.628791\pi\)
−0.393660 + 0.919256i \(0.628791\pi\)
\(762\) 18.0701 0.654611
\(763\) −6.86256 −0.248441
\(764\) −1.13129 −0.0409287
\(765\) 3.22452 0.116583
\(766\) 3.90528 0.141103
\(767\) 11.5319 0.416391
\(768\) −1.80839 −0.0652547
\(769\) 51.1796 1.84558 0.922792 0.385298i \(-0.125901\pi\)
0.922792 + 0.385298i \(0.125901\pi\)
\(770\) 25.0398 0.902372
\(771\) 6.17406 0.222353
\(772\) 0.982429 0.0353584
\(773\) −34.8182 −1.25232 −0.626162 0.779693i \(-0.715375\pi\)
−0.626162 + 0.779693i \(0.715375\pi\)
\(774\) 14.1811 0.509729
\(775\) −14.6820 −0.527395
\(776\) −7.93303 −0.284779
\(777\) 7.02725 0.252101
\(778\) 19.8796 0.712719
\(779\) −9.22346 −0.330465
\(780\) 0.388772 0.0139203
\(781\) 45.3379 1.62232
\(782\) 3.48150 0.124498
\(783\) −1.75504 −0.0627202
\(784\) 24.1498 0.862494
\(785\) 3.22452 0.115088
\(786\) 20.6810 0.737668
\(787\) −43.4460 −1.54868 −0.774341 0.632768i \(-0.781919\pi\)
−0.774341 + 0.632768i \(0.781919\pi\)
\(788\) 0.864171 0.0307848
\(789\) −18.8480 −0.671008
\(790\) 54.7560 1.94813
\(791\) −10.4459 −0.371413
\(792\) 13.7928 0.490104
\(793\) 14.2603 0.506397
\(794\) 31.6297 1.12250
\(795\) −6.65379 −0.235985
\(796\) 0.596927 0.0211575
\(797\) 34.5791 1.22485 0.612427 0.790527i \(-0.290193\pi\)
0.612427 + 0.790527i \(0.290193\pi\)
\(798\) 9.27694 0.328400
\(799\) 11.2096 0.396567
\(800\) 2.30266 0.0814115
\(801\) 6.95174 0.245628
\(802\) 27.3469 0.965654
\(803\) −53.2883 −1.88050
\(804\) 0.970706 0.0342342
\(805\) −8.44341 −0.297591
\(806\) 6.26166 0.220557
\(807\) −7.85901 −0.276650
\(808\) 2.28088 0.0802410
\(809\) −18.4701 −0.649376 −0.324688 0.945821i \(-0.605259\pi\)
−0.324688 + 0.945821i \(0.605259\pi\)
\(810\) 4.64538 0.163222
\(811\) 12.6510 0.444235 0.222118 0.975020i \(-0.428703\pi\)
0.222118 + 0.975020i \(0.428703\pi\)
\(812\) 0.143491 0.00503554
\(813\) 19.5449 0.685469
\(814\) 46.4799 1.62912
\(815\) 38.0759 1.33374
\(816\) −4.14522 −0.145112
\(817\) −58.5002 −2.04666
\(818\) −26.1643 −0.914812
\(819\) 1.73134 0.0604979
\(820\) 0.377612 0.0131868
\(821\) 8.18318 0.285595 0.142797 0.989752i \(-0.454390\pi\)
0.142797 + 0.989752i \(0.454390\pi\)
\(822\) 8.55557 0.298410
\(823\) 15.6202 0.544487 0.272243 0.962228i \(-0.412234\pi\)
0.272243 + 0.962228i \(0.412234\pi\)
\(824\) −8.61918 −0.300264
\(825\) −26.8509 −0.934828
\(826\) −11.2658 −0.391986
\(827\) −34.5939 −1.20295 −0.601474 0.798892i \(-0.705420\pi\)
−0.601474 + 0.798892i \(0.705420\pi\)
\(828\) 0.182348 0.00633705
\(829\) 24.2848 0.843446 0.421723 0.906725i \(-0.361425\pi\)
0.421723 + 0.906725i \(0.361425\pi\)
\(830\) 49.6356 1.72288
\(831\) 15.9152 0.552091
\(832\) 12.2649 0.425209
\(833\) 5.82595 0.201857
\(834\) −31.3099 −1.08417
\(835\) 34.1722 1.18258
\(836\) 2.23081 0.0771542
\(837\) 2.72016 0.0940224
\(838\) 9.77424 0.337645
\(839\) 34.9491 1.20658 0.603288 0.797523i \(-0.293857\pi\)
0.603288 + 0.797523i \(0.293857\pi\)
\(840\) 9.68708 0.334236
\(841\) −25.9198 −0.893787
\(842\) −22.4227 −0.772737
\(843\) 7.55302 0.260140
\(844\) −0.248205 −0.00854355
\(845\) 33.6860 1.15883
\(846\) 16.1491 0.555216
\(847\) 14.8960 0.511833
\(848\) 8.55366 0.293734
\(849\) 2.35210 0.0807240
\(850\) 7.77588 0.266710
\(851\) −15.6730 −0.537263
\(852\) −0.687682 −0.0235596
\(853\) −39.0378 −1.33663 −0.668315 0.743879i \(-0.732984\pi\)
−0.668315 + 0.743879i \(0.732984\pi\)
\(854\) −13.9312 −0.476717
\(855\) −19.1632 −0.655369
\(856\) −29.7084 −1.01541
\(857\) 20.9236 0.714738 0.357369 0.933963i \(-0.383674\pi\)
0.357369 + 0.933963i \(0.383674\pi\)
\(858\) 11.4515 0.390947
\(859\) −2.54949 −0.0869875 −0.0434938 0.999054i \(-0.513849\pi\)
−0.0434938 + 0.999054i \(0.513849\pi\)
\(860\) 2.39502 0.0816696
\(861\) 1.68164 0.0573102
\(862\) −26.2507 −0.894102
\(863\) −30.0634 −1.02337 −0.511686 0.859173i \(-0.670979\pi\)
−0.511686 + 0.859173i \(0.670979\pi\)
\(864\) −0.426617 −0.0145138
\(865\) 49.1217 1.67019
\(866\) −34.2084 −1.16245
\(867\) −1.00000 −0.0339618
\(868\) −0.222398 −0.00754866
\(869\) 58.6377 1.98915
\(870\) −8.15285 −0.276407
\(871\) −20.5558 −0.696506
\(872\) −17.5601 −0.594660
\(873\) −2.86124 −0.0968383
\(874\) −20.6905 −0.699866
\(875\) −1.38881 −0.0469505
\(876\) 0.808273 0.0273090
\(877\) 19.7246 0.666051 0.333026 0.942918i \(-0.391930\pi\)
0.333026 + 0.942918i \(0.391930\pi\)
\(878\) −0.822058 −0.0277431
\(879\) −21.2244 −0.715882
\(880\) 66.4933 2.24149
\(881\) −55.8107 −1.88031 −0.940154 0.340749i \(-0.889319\pi\)
−0.940154 + 0.340749i \(0.889319\pi\)
\(882\) 8.39312 0.282611
\(883\) 40.2068 1.35307 0.676534 0.736411i \(-0.263481\pi\)
0.676534 + 0.736411i \(0.263481\pi\)
\(884\) −0.120568 −0.00405513
\(885\) 23.2715 0.782264
\(886\) −48.0930 −1.61572
\(887\) −51.0012 −1.71245 −0.856226 0.516602i \(-0.827197\pi\)
−0.856226 + 0.516602i \(0.827197\pi\)
\(888\) 17.9815 0.603420
\(889\) 13.5909 0.455824
\(890\) 32.2935 1.08248
\(891\) 4.97469 0.166658
\(892\) 1.14960 0.0384916
\(893\) −66.6185 −2.22930
\(894\) −0.960572 −0.0321263
\(895\) 41.9519 1.40230
\(896\) −12.9064 −0.431173
\(897\) −3.86143 −0.128929
\(898\) −14.0195 −0.467838
\(899\) −4.77400 −0.159222
\(900\) 0.407272 0.0135757
\(901\) 2.06350 0.0687451
\(902\) 11.1228 0.370347
\(903\) 10.6659 0.354938
\(904\) −26.7292 −0.889000
\(905\) 74.8300 2.48743
\(906\) 1.00618 0.0334281
\(907\) 3.88582 0.129026 0.0645132 0.997917i \(-0.479451\pi\)
0.0645132 + 0.997917i \(0.479451\pi\)
\(908\) −0.223149 −0.00740544
\(909\) 0.822654 0.0272857
\(910\) 8.04273 0.266614
\(911\) −42.0118 −1.39191 −0.695956 0.718084i \(-0.745019\pi\)
−0.695956 + 0.718084i \(0.745019\pi\)
\(912\) 24.6349 0.815745
\(913\) 53.1543 1.75915
\(914\) 3.84069 0.127039
\(915\) 28.7775 0.951355
\(916\) −0.150831 −0.00498360
\(917\) 15.5546 0.513658
\(918\) −1.44064 −0.0475483
\(919\) −41.3234 −1.36313 −0.681567 0.731755i \(-0.738701\pi\)
−0.681567 + 0.731755i \(0.738701\pi\)
\(920\) −21.6052 −0.712303
\(921\) 26.0338 0.857844
\(922\) −34.1313 −1.12406
\(923\) 14.5624 0.479328
\(924\) −0.406726 −0.0133803
\(925\) −35.0053 −1.15097
\(926\) 9.45981 0.310869
\(927\) −3.10872 −0.102104
\(928\) 0.748732 0.0245783
\(929\) −36.3212 −1.19166 −0.595830 0.803110i \(-0.703177\pi\)
−0.595830 + 0.803110i \(0.703177\pi\)
\(930\) 12.6362 0.414356
\(931\) −34.6235 −1.13474
\(932\) 0.385217 0.0126182
\(933\) −2.02959 −0.0664457
\(934\) 14.8291 0.485221
\(935\) 16.0410 0.524596
\(936\) 4.43020 0.144806
\(937\) −36.5702 −1.19470 −0.597348 0.801982i \(-0.703779\pi\)
−0.597348 + 0.801982i \(0.703779\pi\)
\(938\) 20.0815 0.655684
\(939\) 1.69194 0.0552143
\(940\) 2.72739 0.0889576
\(941\) −29.7322 −0.969244 −0.484622 0.874724i \(-0.661043\pi\)
−0.484622 + 0.874724i \(0.661043\pi\)
\(942\) −1.44064 −0.0469387
\(943\) −3.75059 −0.122136
\(944\) −29.9163 −0.973693
\(945\) 3.49388 0.113656
\(946\) 70.5466 2.29367
\(947\) −4.74210 −0.154098 −0.0770488 0.997027i \(-0.524550\pi\)
−0.0770488 + 0.997027i \(0.524550\pi\)
\(948\) −0.889412 −0.0288868
\(949\) −17.1161 −0.555612
\(950\) −46.2119 −1.49931
\(951\) −17.8299 −0.578173
\(952\) −3.00420 −0.0973666
\(953\) −23.1658 −0.750413 −0.375207 0.926941i \(-0.622428\pi\)
−0.375207 + 0.926941i \(0.622428\pi\)
\(954\) 2.97277 0.0962469
\(955\) 48.3445 1.56439
\(956\) −1.78868 −0.0578500
\(957\) −8.73081 −0.282227
\(958\) −51.9002 −1.67682
\(959\) 6.43481 0.207791
\(960\) 24.7508 0.798830
\(961\) −23.6007 −0.761314
\(962\) 14.9292 0.481337
\(963\) −10.7151 −0.345288
\(964\) 2.23791 0.0720783
\(965\) −41.9830 −1.35148
\(966\) 3.77234 0.121373
\(967\) 2.56051 0.0823406 0.0411703 0.999152i \(-0.486891\pi\)
0.0411703 + 0.999152i \(0.486891\pi\)
\(968\) 38.1163 1.22510
\(969\) 5.94298 0.190916
\(970\) −13.2916 −0.426766
\(971\) 17.7103 0.568350 0.284175 0.958773i \(-0.408280\pi\)
0.284175 + 0.958773i \(0.408280\pi\)
\(972\) −0.0754557 −0.00242024
\(973\) −23.5488 −0.754938
\(974\) 41.9507 1.34419
\(975\) −8.62444 −0.276203
\(976\) −36.9944 −1.18416
\(977\) −7.90255 −0.252825 −0.126413 0.991978i \(-0.540346\pi\)
−0.126413 + 0.991978i \(0.540346\pi\)
\(978\) −17.0115 −0.543967
\(979\) 34.5828 1.10527
\(980\) 1.41750 0.0452804
\(981\) −6.33348 −0.202212
\(982\) −26.2251 −0.836876
\(983\) −24.8779 −0.793483 −0.396741 0.917930i \(-0.629859\pi\)
−0.396741 + 0.917930i \(0.629859\pi\)
\(984\) 4.30303 0.137176
\(985\) −36.9294 −1.17667
\(986\) 2.52839 0.0805205
\(987\) 12.1460 0.386612
\(988\) 0.716531 0.0227959
\(989\) −23.7883 −0.756423
\(990\) 23.1093 0.734463
\(991\) −1.10168 −0.0349959 −0.0174979 0.999847i \(-0.505570\pi\)
−0.0174979 + 0.999847i \(0.505570\pi\)
\(992\) −1.16047 −0.0368448
\(993\) 32.7132 1.03812
\(994\) −14.2264 −0.451235
\(995\) −25.5090 −0.808689
\(996\) −0.806239 −0.0255467
\(997\) 3.04994 0.0965926 0.0482963 0.998833i \(-0.484621\pi\)
0.0482963 + 0.998833i \(0.484621\pi\)
\(998\) 23.4455 0.742155
\(999\) 6.48548 0.205191
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8007.2.a.f.1.14 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.14 48 1.1 even 1 trivial